Question 92

In the given figure, PQRS is a rectangle and PTU is a triangle. If PQ = 11 cm, UR = 8 cm, TR = 1 cm and QT = 3 cm, then what is the length (in cm) of the line joining the mid points of PT and TU?

Solution

Length of rectangle PQ = 11 cm and breadth = QR = 4 cm

=> SU = 3 cm and PS = 4 cm

Thus, in $$\triangle$$ PSU,

=> $$(PU)^2=(PS)^2+(SU)^2$$

=> $$(PU)^2=(4)^2+(3)^2=16+9$$

=> $$PU=\sqrt{25}=5$$ cm

$$\because$$ M and N are mid points of PT and TU respectively, => $$MN=\frac{1}{2} PU$$

= $$\frac{1}{2}\times5=2.5$$ cm

=> Ans - (A)

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